Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x - 9$ and $ BC = 5x + 9$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x - 9} = {5x + 9}$ Solve for $x$ $ 2x = 18$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({9}) - 9$ $ BC = 5({9}) + 9$ $ AB = 63 - 9$ $ BC = 45 + 9$ $ AB = 54$ $ BC = 54$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {54} + {54}$ $ AC = 108$